USAAAO 2015, II кръг — Задача 12

This is the Second Round of the 2014-2015 USA Astronomy and Astrophysics Olympiad (USAAAO) competitions. You have exactly 2 hours and 30 minutes to complete the exam. There is a maximum of 67 points, and the value of each problem is indicated following each problem statement.

This test consists of 13 short answer problems and one long problem with multiple parts. Solutions should be written on blank paper, with the problem number, student’s name, and school written clearly on top of each page. Solutions to multiple short answer problems may be written on the same page, but the long problem should begin on its own page. Partial credit will be given for correct work, so make sure to clearly show all steps.

You may only use a scientific calculator as aid for this exam. A table of physical constants and other information will be provided for you. This exam document, your solutions, and all used scratch paper must be turned in at the end of the exam.

Do not discuss this examination with anyone after its completion. Your results will be emailed to you shortly. The top 5 students will be invited to represent the United States at the 9th International Olympiad on Astronomy and Astrophysics competition in Central Java, Indonesia, from July 26th to August 4th, 2015.

In the event of a tie for the top 5 places, the student with the higher score on the long problem will qualify. If the tied students have the same score on the long problem, then the short answer problems with more points will be given more weight in the grading.

I hereby affirm that all work on this exam is mine, and that I took this test under a proctor’s supervision, with no outside aids beyond the materials provided and allowed. Furthermore, I affirm to not discuss the test with others or provide any sort of aid to other examiners throughout the course of the examination period. I understand that failure to do so may result in disqualification from the exam.

Signature: ____________________________________________ Date: ____________________